Less than 24 hours after Ohio State suffered its first loss in two seasons, a fall that took the Buckeyes out of the last Bowl Championship Series title game, they gained a formal invitation to take on Clemson in the 80th Orange Bowl on Jan. 3 in Miami Gardens, Fla.

As far as OSU coach Urban Meyer is concerned, it is quite the consolation prize for the Buckeyes (12-1), who lost to Michigan State in the Big Ten title game late Saturday in Indianapolis and fell to No. 7 in the final BCS standings.

“They’re heartbroken, but they are also competitors,” Meyer said. “And I think the fact we are playing in a BCS bowl game against Clemson, that’s going to wake you up real fast. … There’s no doubt in my mind we’ll be excited to go play in this bowl game.”

It’s a matchup that not only has historic ramifications for the Buckeyes, but also one that could set the bowl game’s offensive record book spinning. The Buckeyes, led by prolific dual-threat quarterback Braxton Miller and powered by 1,400-yard rusher Carlos Hyde, sport one of the elite running games in the country. Clemson’s explosive offense orchestrated by Tajh Boyd and featuring big-play threat Sammy Watkins is one of the premier passing teams in the nation.

Now, throw in the fact that both teams have played sketchy defense from time to time this season, and the stage is set for a shootout.

“We expect a game featuring offensive fireworks, since both teams average more than 40 points a game,” Orange Bowl CEO Eric Poms said.

Ohio State and Clemson (10-2) are at-large picks. The Orange Bowl took the Tigers, No. 12 in the BCS, to fill the slot usually reserved for the Atlantic Coast Conference champion. Florida State won the ACC but is playing Auburn in the BCS title game.

In the 15 years of the BCS, this will be Ohio State’s 10th appearance in a BCS game (although the 2010 Sugar Bowl victory over Arkansas was vacated because of NCAA sanctions). But this will be just the second game between OSU and Clemson, and most OSU fans know what happened near the end of the first one, in the 1978 Gator Bowl. Won by Clemson, the game also was the last one for Woody Hayes, the winningest coach in OSU history. He was fired after losing his cool late in the game and punching Clemson player Charlie Bauman, who had run out of bounds in the Buckeyes’ bench area after intercepting an OSU pass.

It will be just the second appearance in the Orange Bowl for Ohio State, which defeated Colorado there after the 1976 season.

Clemson will be in the Orange for the second time in three years.

“It’s a great credit to our team, how they’ve competed, and the consistency we’ve developed within our program,” said Clemson coach Dabo Swinney, whose team’s two losses this year were to FSU and in the regular-season finale against instate rival South Carolina.

“We look forward to a great game against one of the best teams in the country in Ohio State,” Swinney said. “There are a lot of great players heading down to South Beach to compete in a good one, I’m sure.”

The challenge for Ohio State, obviously, is shoring up a pass defense whose porosity played a major role in leading to the team’s first loss in two seasons on Saturday night, giving up more than 300 yards passing to a Michigan State team not known for its aerial game. And that came just a week after Michigan laced OSU’s defense for more than 400 yards passing.

Clemson comes out of the tunnel throwing the ball, which was why at one point this season Boyd was considered a major contender in the Heisman Trophy race. But FSU and quarterback Jameis Winston — now the heavy favorite — knocked off the Tigers.

“There’s certainly things we’ve got to get fixed, and get fixed in a hurry,” Meyer said. “Look what’s coming down the road here.”